orbit - How (un)stable are the Lagrangian points 1, 2 and 3?

All five Lagrange points are unstable

L1, 2, and 3 are "saddle points" in the effective potential formed from the combination of gravity and the centrifugal force of a rotating frame of reference. An object which is in front or behind in the orbit would tend to approach the Lagrange point, and then move away, either towards or away from the sun, following the lines in the picture.

However note that in the picture, the lines around the Lagrange points are not close together, this means that the motion towards, or away from the point is very slow (in the rotating frame) An object near the Lagrangian point would not be "ejected" at high speed. Any cosmic dust that was near the Lagrangian point would drift slowly away.

However although the L4 and L5 points are unstable, there are quite stable orbits that (in the rotating frame) orbit around the L4 and L5 point, allowing for Trojan satellites.